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%I #27 Dec 18 2023 10:06:01
%S 0,0,6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6,4,
%T 1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,
%U 6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6,4,1,0,2,5,6
%N Decimal expansion of 1/156.
%H Colin Barker, <a href="/A021160/b021160.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,1).
%F The period is just 6: after 0.00, 641025 repeated endlessly. - _Alonso del Arte_, Apr 18 2018
%F From _Colin Barker_, Apr 19 2018: (Start)
%F G.f.: x^2*(6 - 8*x + 5*x^2) / ((1 - x)*(1 - x + x^2)).
%F a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n>4. (End)
%e 0.00641025641025641025641025641...
%t PadRight[{0, 0}, 100, {2, 5, 6, 4, 1, 0}] (* or *) Join[{0, 0}, RealDigits[1/156, 10, 100][[1]]] (* _Harvey P. Dale_, May 13 2012 *)
%o (PARI) 1/156. \\ _Altug Alkan_, Apr 18 2018
%o (PARI) concat(vector(2), Vec(x^2*(6 - 8*x + 5*x^2) / ((1 - x)*(1 - x + x^2)) + O(x^60))) \\ _Colin Barker_, Apr 19 2018
%Y Cf. A021043 (1/39).
%K nonn,cons,easy
%O 0,3
%A _N. J. A. Sloane_
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